Taking horizontal ground as `xz`- plane and y-axis vertically upwards. A particle is projected from the horizontal ground from a point whose position vector is `hati_hatk` meter with initial velocity from the origin when it hits ground is given by `(1)/(5)[11hati+n hatk]`, find `n`. (Take `g = 10 m//s^(2)` in negative y - direction)

Answer

8

Explanation

Taking horizontal ………….
`a = -10 hatj`
`vec r_(2) = vec r_(1)+vec u t+(1)/(2)veca t^(2)`
`vec r_(2) = (hati + hat k) + (2hati + 3hat j+hat k)t-5hatj t^(2)`
`vec r_(2) = (1+2t)hati + (3t-5t^(2))hatj+(1+t)hatk`
When particle lands on ground
`3t - 5t^(2)= 0 implies t = (3)/(5)s`
`vec r_(2)= (11)/(5)hati + (8)/(5)hatk`